Caminao Ontological Kernel (Protégé/OWL 2) (WIP)

As long as philosophy is concerned, ontologies are meant to distinguish between realms of knowledge and their description through languages.

mantegna — What they see is what you get (Mantegna)

And yet, most present-day ontologies overlook that distinction, and consequently confuse the nature of objects and phenomenons (concrete or symbolic) with the open-ended range of their representations by human minds.

Preamble

While ontologies are often reduced to the extended graph-based thesauruses and semantic networks used in business intelligence, the immersion of enterprises into digital environments calls for a broader understanding of ontologies that would ensure a seamless integration of data analytics, information systems, and knowledge based decision-making. That can be best achieved through an ontological approach to enterprise architecture frameworks.

In contrast to systems architecture, enterprise architecture must maintain a continuous and consistent representation of business environments and objectives because:

Architectural changes must be carried out without impairing business
Environments may change in parallel with engineering processes

These requirements can be best satisfied through comprehensive ontologies, and that’s the objective of the Caminao kernel developed with OWL 2. A beta version is available for comments on the Stanford/Protégé portal with the link Caminao Ontological Kernel (Cake_Diner).

Objective

From a conceptual perspective the objective is to demonstrate the benefits of the Stanford modeling paradigm that defines systems as containers managing symbolic representations (aka surrogates) of operational environments.

From a functional perspective the kernel is to meet the principles of knowledge representation set by Davis, Shrobe, and Szolovits in their seminal article:

Surrogate: KR provides a symbolic counterpart of actual objects, events and relationships.
Ontological commitments: a KR is a set of statements about the categories of things that may exist in the domain under consideration.
Fragmentary theory of intelligent reasoning: a KR is a model of what the things can do or can be done with.
Medium for efficient computation: making knowledge understandable by computers is a necessary step for any learning curve.
Medium for human expression: one the KR prerequisite is to improve the communication between specific domain experts on one hand, generic knowledge managers on the other hand.

Traditional models can support points 1, 4 and 5, but fall short of points 2 and 3. Ontologies are meant to generalize the representation of and reasoning about any number of realms, actual or virtual. The aim of the kernel is to bring under a common roof the whole of representations pertaining to enterprises governance.

CaKe_archi — Caminao Ontological Kernel in Context

Ontologies, Models, & Thesauruses

The contents of ontologies can be formally defined in terms language, models and thesaurus:

Thesauruses define the meaning of terms, categories, and concepts.
Models add syntax to build representations of contexts and concerns.
Ontologies add pragmatics in order to put models in broader perspectives.

These levels correspond to the epistemic nature of the targeted elements:

Concepts: pure semantic constructs defined independently of instances or categories
Categories: symbolic descriptions of sets of objects or phenomena: Categories can be associated with actual (descriptive, extensional) or intended (prescriptive, intensional) sets of instances
Facts: observed objects or phenomena
Documents: entries for documents represent the symbolic contents, with instances representing the actual (or physical) documents

Besides concepts and documents, which correspond to thesaurus and content management systems (CMS), the backbone of the kernel is built around categories of actual and symbolic entities.

Kernel Organization

Aspects & Properties

Descriptions without external instances of their own: aspects cannot be directly instantiated (or identified) in environments; they can only exist as digital components in systems. Since they are not meant to directly represent individuals in domains, aspects can be defined in terms of standard generic of functional constructs, ensuring interoperability with modeling languages:

Features (Properties and operations).
Numeric and logic expressions.
Abstract data types (collections, graphs, …)
States (lifecycles)

With OWL 2, the kernel defines aspects in the Class hierarchy, but connectors are defined as object properties, and attributes as data properties.

Contrary to categories, whose instances are to be checked for external consistency, aspects have only to be checked for internal consistency.

Kernel properties

Connectors being the glue of knowledge, their semantics is to make the difference. On that account, the primary objective should be to set apart thesaurus and modeling connectors from ontological ones. That can be achieved through linguistic layers.

Syntax Connectors

Syntactic connectors are set at the representation level independently of semantics and pragmatics. Generic ones coincide with established modeling standards for collections, aggregates, and compositions; they are meant to be executable and support truth-preserving operations independently of domain semantics.

Category Connectors

Category connectors apply to descriptions: categories, types, classes, etc.

Structure connectors (include_) deal with composition
Variant connectors deal with functional (extendedBy_, extensionOf_) and structural (subset_, subsetOf_) hierarchies
Sorting connectors (sortedBy_) deal with partitions

Instance Connectors

Instance connectors apply to the representation of individuals, i.e., identified occurrences of objects (connectRefer_) or behavior (connectExec_) descriptions.

Semantic Connectors

Semantic connectors deal with the specifics of business domain and enterprise architecture. The kernel comes with a basic set of architecture and engineering connectors.

Architecture Connectors

Architecture connectors are meant to describe functional and technical capabilities and dependencies independently of business domains semantics:

Interdependencies between capabilities at the enterprise level: roles, objects, activities, locations, events and processes.
References between symbolic representations.
Flows between activities: passive symbolic or actual content, or active requests.
Dependencies between processes execution.
Communication channels between objects or locations according to capabilities: physical, digital, or symbolic.

Engineering Connectors

Beside the representation of standard engineering flows (refObjective_, refResource_, refOutcome_), the kernel introduces ontological connectors to deal with the mapping of representations across epistemic levels:

Between symbolic representations within organizations (realizeX_)
Between symbolic or non-symbolic external objects or phenomena and their symbolic counterpart within organizations (mapTerritX_)

Ontology Connectors

Ontology connectors are meant to bring together the whole range of representations.

Axioms

To be ecumenical and ensure perennial conceptual interoperability across domains and organizations, definitions are built on a limited set of unambiguous and effective axioms:

Limited: since axioms serve as roots to acyclic semantic graphs, there should be as few axioms as possible.
Unambiguous: axioms are meant to be either accepted or rejected, which implies that their meaning should be clear and leave no wiggle room for misunderstanding.
Effective: the axioms singled out are not meant to be the pillars of some absolute truth, but rather to serve as logical hubs for sound and effective EA categories. They should therefore only be judged on their effectiveness in supporting clear and concise EA definitions.

Taking exemple on music keys, and assuming standard logic, ten axiomatic definitions are introduced as modeling primitives:

Instances

Physical, digital, or symbolic occurrences of objects or phenomena (both accepted as postulates): The distinction between physical, digital, and symbolic instances is not exclusive (consider hybrids); additionally, fictional instances are instances (physical or symbolic) that are not meant to be realized. Instances are represented by individuals in OWL.

Attributes

Characteristics of instances that belong to them and make them recognisable.

Collection

Set of individuals managed uniformly, independently of their nature.

Identity

Unique value associated with individuals: External identities are defined independently of the organization or system under consideration. External identities can be biological, social, or designed; they are not exclusive (e.g., social security number and fingerprints). Internal identities are used to manage individuals within organizations or systems independently of environments.

Symbolic Representations

Borrowing from semiotics:

A symbol is a sign pointing to something else (referent).
A symbolic representation is a symbol pointing to a set of instances.
A symbolic object is an object representing a referent; this means that symbolic objects can be physical, as they usually are.

Behavior

The ability of an instance to change the state of instances, including itself: Objects are either active (with behavior) or passive (without behavior), and the propriety is exclusive.

State

Named sets of values that characterize instances of objects (actual or symbolic), processes, or representations, between events. Stateful objects and activities come with a finite number of discrete states; stateless ones don’t have this limited array, and may indeed have an infinite number of discrete states.

Event

Change in the state of objects and phenomena: External events are changes triggered from outside the organization or system under consideration.

Thesaurus Connectors

Axioms serve as roots and firebreaks in acyclic semantic networks of definitions. Axiomatic definitions are not meant to be “true,” comprehensive, or exclusive; but rather, effective (to make a difference), as simple as possible (Occam’s razor), and open to refutation.

Basic ones (thesaurusBw_ and thesaurusFw_) put the focus on semantic dependencies, ensuring that there is no circular definitions. Semiotic ones deal mirror OWL2 references for synonyms, homonyms, and antonyms.

Combined with OWL 2 hierarchies, these semantic networks constitute the kernel of the thesaurus, which can then be fleshed out to build EA Knowledge graphs.

Given the layered organization (axioms and acyclic networks for semantics, and graphs for EA knowledge), consistency checks can be formal with regard to the kernel (e.g., no circular definitions), but pragmatic and customized with regard to EA definitions.

Inference Connectors

Inference connectors provide a basic set of logic operators, to be fully implemented through OWL 2 properties assertions:

Universal (infUQuantifier_), existential (infEQuantifier_) and negative infNQuantifier_) quantifiers
Forward and backward nondescript inferences
Inferences from analogies (infAnalogy_ and contiguities (infContiguity_)

Combined with partitions and powertypes, inference connectors can be used at domain or category level.

Combined with composition and reference connectors inference ones can also be used to define business logic, e.g.:

Constraints on bank accounts’ overdrafts
Data-driven (pull) rule: If (overdraft) Do (notification)
Event-driven (push) rule: When (forcible entry) Do (trigger alarm)

Annotations properties

Beside basic modeling annotations for interoperability, the kernel introduces ontological ones to characterize epistemic modalities:

Temporal: Past, present, planned, expected
Existential: Prohibited, impossible, permitted, possible, mandatory, necessary, exempted, elective
Narrative: Actual, virtual, fictional

Kernel Integration

The primary aim of ontologies is to bring under a single roof three tiers of representations and to ensure both their autonomy and integrated usage:

Thesauruses federate meanings across digital (observations) and business (analysis) environments
Models deal with the integration of digital flows (environments) and symbolic representations (systems)
Ontologies ensure the integration of enterprises’ data, information, and knowledge, enabling a long-term alignment of enterprises’ organization, systems, and business objectives

From a technical perspective the consistency and interoperability of those tiers can be achieved using graphical neural networks (GNN) and Resource description framework (RDF).

Ontologies Integration & Interoperability

From a functional perspective ontologies must support the strategic alignment of enterprises’ business objectives and architectures materialized by operations and organization.

To provide a basis to user access the kernel comes with a number of generic filters:

Negative filters operate on nodes and are used to mask root categories, e.g.: xActivities, xObjects
Basic hierarchy filters (1,2,3) operate selectively on OWL subclass and instance properties
Hierarchy4 filter operates on kernel variant properties, e.g.: subset_, extendedby_
Association and composition filters operate selectively on structural (include_) and functional (connectRef_, connectExe_) kernel properties
Thesauruses and inference connectors operate selectively on semiotic and reasoning kernel properties

These filters can be used to define integrated views according to perspective.

Ontologies as Glue between Meanings & Purposes

Thesauruses & Ontologies

Contrary to a naive understanding, there can be no universal attachment of words to reality, even for concrete objects; and business affairs are generally more symbolic than actual. For enterprises’ ontologies the primary objective is therefore to manage the various meanings associated with environments’ objects and phenomena whatever their nature (concrete or symbolic) and naming source (external or internal). That’s the role of thesauruses.

From a business perpective, thesauruses are used to attach names to data taking into account the specificities of business domains and the heterogeneity of sources. The focus is put on the federation of data semantics across sources and business domains (data meshes).
From a system perspective thesauruses are used to map named data to their employ by applications and functions. The focus is put on the consolidation of business domains’ semantics and shared resources, meta-data, and master data management (MDM).

The integration of thesauruses within ontologies can be achieved through their refactoring as semantic networks and the replacement of semantic connectors (aka connecting nodes) with syntactic ones, e.g.:

Removing semantics from connectors between thesauruses nodes has two consequences:

Syntactic connectors can only be interpreted in business specific contexts
They can be uniformly defined as to ensure syntactic interoperability across modeling languages

The benefits of such normalized thesauruses can be demonstrated by their integration with Entity-relationship (E/R) and Relational data models.

Models & Ontologies

Whereas thesauruses put the focus on meanings, i.e. the attachment of words to facts and ideas, the primary objective of models is to manage representations:

From a business perspective, models are used to define processes and plan for changes in environments
From a system perspective, they are used to define architectures and support engineering (MBSE).

But facts are not manna ready to be picked: to ensure a perennial and consistent representation of objects and phenomena observations must be structured and put into contexts; that is done by adding syntax (for structures) and semantics (for contexts and concerns). Models can then serve to align enterprises’ environments and objectives on the one hand, organization and supporting systems on the other hand.

Identities, Structures, Aspects

The distinction between thesauruses and models takes a particular importance for enterprises immersed in digital environments as it marks the limit between unregulated concerns (the meanings of words) and regulated ones (business objects), with models serving as gate keepers between observed data and managed information. To that effect models must extend thesauruses with identities and structures:

Since representations are meant to associate concepts or categories (as defined in thesauruses) to sets of objects or phenomenas, some principle is required to identify relevant individuals.
Then, a distinction must be maintained between intrinsic (or structural) features of individuals on the one hand, and functional or behavioural ones on the second hand.
Finally, constraints must be added with regard to the structural and functional integrity of representations.

Leading modeling languages (E/R, Relational, and OO) come with the relevant syntactic constructs and the objective of the kernel connectors defined above is to provide a common unambiguous subset.

Assuming homogenous domains for identification and semantics, transitions from normalized thesauruses to models would be straightforward using ontological connectors. Not so for abstractions defined in thesauruses.

Semantics & Abstractions

As long as abstractions are about meanings they can be understood in terms of “kind of” or “is a” relationships without actual consequences. That’s the way abstractions are represented in OWL2 (yellow color). But that understanding falls short if abstractions are applied to representations, as they are supposed to be in models. In that cases semantics are meant to vary with the kind of abstraction:

Conceptual, as defined in thesauruses (yellow color)
Structural and functional, represented by subsets and extensions respectively (blue color)

Thesauruses should thus be extended as to take into account the semantics of structural and functional abstractions; that is done with the subset_ and extend_ connectors, respectively.

One step further, thesauruses could include explicit partitions (sortedBy_) that would directly translate as modeling powertypes, to be realized through instances (MusicInstr2Source) or subtypes (MusicInstr2Function).

That unified representation of abstractions in terms of subtypes and instances ensures a seamless integration of models within ontologies.

Ontologies & Knowledge

To get a competitive edge in digital environments, enterprises have to read through a massive and continuous flow of data and information, a task that involves three intertwined undertakings:

Reducing uncertainty (observation): facts are not manna from heaven ready to be observed but have to be mined from qualified data.
Determining causal chains (orientation): while predicate logic and statistical inference may suffice with single root causes, they may lose their way in causal mazes.
Managing risks (decision): since business competition is by nature a time- dependent, nonzero-sum game, decision-making processes must weigh orientations with a dynamic assessment of risks, and balance business opportunities with the sustainability of architectural assets.

Sorting out these undertakings into manageable threads can be best achieved through iterations of the OODA loop backed by ontologies integrating forms (thesauruses, models, graphs), contents (data, information, knowledge), and functions (observation, reasoning, decision-making).

Observation: From Data to information:

The raison d’être of ontologies is to make explicit the relationship between languages and what they denote; for enterprises trying to make sense of continuous and massive flows of observations, using ontologies removes a double delusion:

The implicit assumption that meanings can be extracted from raw data like gold nuggets from river beds independently of customary contexts and purposes
The explicit assumption that concepts can be organized into final and universal hierarchies

Machine learning is used to make sense of unstructured observations obtained from environments (Data mining) and operations (Process mining). Put simply, the objective is to map data into hypothetical categories in combining three operations: identification of relevant items, definition of boxes, assessment and improvement of mappings. Optimized boxes can thus translate into meaningful categories used to build information models.

That twofold undertaking corresponds to the distinction between data analytics and data analysis, the former for marketing data (e.g. profiles of anonymous music listeners), the latter for managed information (e.g., ticket sales). It also corresponds to key governance distinctions:

Between unregulated observations and regulated managed information
Between the intrinsic uncertainties of observations and the necessary reliability of models

Knowledge graphs are introduced to manage the transitions, e.g. to explore opportunities or define strategies.

Orientation: From information to knowledge

Beside their role as backbone and glue, knowledge graphs add two key capabilities to thesauruses and models:

Built-in epistemic levels of representation, e.g., actual, virtual, planned, expected, etc.
Reasoning capabilities, in particular with regard with modal logic and traceability.

Epistemic Levels

Being limited to meanings, thesauruses can only deal with logical inferences, not with inferred realms. Similarly, while modeling domains can be used to manage different kinds of contexts, their integration must be done through programming, as illustrated by the Ubiquitous language (UL) of Domain driven design (DDD).

Hence the need to manage resources (data and information) according to their nature while ensuring the integration of truth-preserving and heuristic processing. That can be achieved by adding logic connectors and reasoning patterns to models, establishing a bridge between epistemic levels.

Taking the Parent/Children exemple, logic can deal with the fact that persons have parents, and models can represent corresponding individuals and relationships, e.g.:

Entity Person_ with instance Mike,
Role Parent() with standard connector (connectRef#_)
Logical connector (infUQuantifier_) for universal constraint

But unidentified instances and associated relationships cannot be explicitly represented by models; to that end epistemic levels are needed, e.g.:

Mike‘s deduced instance of Parent() with standard connector (connectRef_)
Induced (not observed) instance JDoe of Person_
Unidentified connector (connectRef?_) for Mike’s physical parent

That simple exemple illustrates the significance of epistemic levels with regard to the distinction between data (JDoe) and information (Mike), and its benefits with regard to the management of privacy regulations.

Reasoning Capabilities

In principle, reasoning with models can be achieved through computation (functions), deduction (dependencies), and induction (statistics). In practice the benefits are limited by the lack of epistemic levels

Decision: Collective Knowledge & Organization

If anything, the ultimate benefit of ontologies is to enable the weaving of individual knowledge threads into a collective fabric mixing systems and organizational capabilities.

That pivot from learning (individual and collective knowledge) to decision- making (individual accountability) is arguably a critical issue for organizations.

Caminao Ontological Kernel (Protégé/OWL 2) (WIP)